It is known for a tire sensor module to be arranged on a tire inner side of a vehicle tire, which tire sensor module can determine characteristic variables of the vehicle tire, for example a tire pressure or a tire temperature, and can transmit these via a radio signal to a control unit. Furthermore, a tire sensor module of the type can also detect an acceleration, wherein, in particular, a radial acceleration of the tire inner side can be determined. From the radial acceleration, it is possible not only to determine a motion state of the vehicle tire but also to draw conclusions regarding a profile depth of a tire profile of the vehicle tire, by virtue of the profile of the radial acceleration being evaluated over a time period or over a traversed rolling circumference. A disadvantage of previous evaluation methods is that the determination of the profile depth is highly inaccurate in particular in the case of a worn vehicle tire, that is, in the case of a small profile depth.